REVIEW 3 major objections 5 minor 8 references
A greedily selected subset of a language model's components outperforms the full gradient and random projection at retrieving the training examples that influenced a prediction.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · deepseek-v4-flash
2026-08-03 08:29 UTC pith:CG22D2SS
load-bearing objection The benchmark and single-component analyses are useful, but the headline 'select beats project' claim is an in-sample fit. the 3 major comments →
Select or Project? Evaluating Lower-dimensional Vectors for LLM Training Data Explanations
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The paper's central claim is that when gradients must be compressed to make instance-based explanations tractable, deliberately choosing a small set of model components beats both the uncompressed full gradient and indiscriminate random projection. To test this, the authors construct a retrieval benchmark: a query sample (a paraphrase of a training point, or a model-generated completion on a paraphrased prompt) must be matched to its original among five candidates. They then greedily add the component—of 113 distinct tensors in a 1.2B-parameter decoder-only transformer—that most improves retrieval accuracy, exploiting the fact that the cosine similarity of any subset of components can be rec
What carries the argument
The central mechanism is the linearity of the dot product over concatenated component gradients: the cosine similarity for any subset of components can be reconstructed exactly by summing precomputed per-component dot products. This lets the greedy forward search—which iteratively adds the component yielding the largest retrieval-accuracy improvement—operate entirely on scalar values, avoiding materialization or storage of high-dimensional gradient vectors.
Load-bearing premise
The load-bearing premise is that higher cosine similarity between a query's gradient and its true original's gradient—compared with other training samples—actually indicates training-data influence; the paper states this assumption in Section 3.2, and if it fails, retrieval accuracy measures generic gradient similarity rather than explanation quality.
What would settle it
Take a fixed query and its known original among five candidates and run the greedy selection; if a randomly chosen subset with the same parameter budget reaches the same retrieval accuracy as the greedy subset, the selection signal is doing no work. Alternatively, if the full gradient retrieves the true original accurately in cases where the selected subset fails, the noise-filtering claim is not general.
If this is right
- For retrieval-style training-data attribution, targeted component selection is preferable to random projection and to the full gradient as a source of gradient representations.
- The full gradient is not the best available representation; filtering out noisy components improves retrieval accuracy, nearly doubling it in the harder model-generated setting.
- A component's functional role matters more than its parameter count: MLP gate/up and attention Q/O projections carry the signal, while attention K/V projections perform near or below random chance.
- The proposed benchmark is re-training free, local, static, and model-invariant, so it can be reused to evaluate other compression and attribution methods.
- Architecture-aware selection reduces compute by orders of magnitude relative to random projection, making gradient-based explanations of large models more feasible in practice.
Where Pith is reading between the lines
- Beyond the paper: the same greedy selection strategy could be applied to other gradient-comparison methods, such as influence functions, data Shapley, or data pruning, where full-gradient comparisons are prohibitive; the retrieval proxy would then need to be validated against true leave-one-out influence.
- Beyond the paper: the experiments cover only one 1.2B-parameter model and one fine-tuning dataset; a natural test is whether the selected components (early/late layers, MLP-heavy) transfer across architectures, scales, and domains, or whether selection must be re-run per task.
- Beyond the paper: the non-monotonic accuracy-versus-parameter-budget curve suggests an optimal budget per task; a practical extension would be a stopping rule that selects components until retrieval accuracy plateaus rather than using a fixed parameter fraction.
- Beyond the paper: random projection preserves the full gradient's geometry but not retrieval performance, so the benchmark measures task-specific discriminative signal rather than geometric fidelity; making this distinction explicit could guide future compression objectives.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper addresses the practical problem that gradient-based training data attribution for LLMs is computationally prohibitive in full parameter space. It proposes a retrieval benchmark in which the gradient of a paraphrased or model-generated query must be matched to its original training sample among BM25-selected distractors. The authors compare three representations: the full gradient, a random projection baseline, and a greedy component-selection method (Select) that incrementally adds the model component that most improves retrieval accuracy. Using a 1.2B OLMo model and 988 LIMA samples, they report that the greedy selection outperforms both the full gradient and random projection in retrieval accuracy, and that it is computationally cheaper than random projection. The paper also provides per-component analyses showing that MLP and attention Q/O components are more informative than K/V components, and that early and late layers dominate in the model-generated setting.
Significance. If the central comparison were valid, this would be a useful contribution to instance-based explainability: it systematically evaluates a practical design choice (select vs. project), introduces a reusable benchmark, releases code, and leverages the linearity of dot products to make subset selection efficient. The per-component findings are interesting and could guide practitioners. However, the headline claim currently rests on an evaluation protocol that fits the selection criterion to the same data used to report accuracy. The evidence for the claimed superiority of Select over full gradients and random projection is therefore not established by the current experiments. A held-out evaluation is needed before the results can be interpreted as generalizable findings.
major comments (3)
- [§3.3 (Algorithm 2) and §5.3 (Figure 4)] The reported retrieval accuracies for Select are in-sample fits. Algorithm 2 greedily chooses each component by maximizing acc(b) on the exact query sets Dp/Dm and the exact candidate sets Ci(b) that are later used to plot Figure 4. No train/validation split is described in Section 4 or 5, and the paper does not mention any form of nested evaluation. With 113 components and 988 queries, the selector can exploit idiosyncrasies of the particular paraphrase/generation instances. The contrast with the model-generated setting—full gradient 0.218 vs. random baseline 0.2, selected subset 0.36—is especially suggestive of noise fitting. The authors must evaluate Select on held-out queries/candidates (e.g., select on one subset, report on a disjoint subset) before claiming that a selected subset 'captures information' better than full gradients or random projection.
- [§3.3 vs. §3.4 and Figure 4] The comparison is not apples-to-apples. The greedy selector is explicitly label-informed: it is optimized on the same retrieval task used for reporting. Random projection and the full gradient are fixed representations with no access to the task labels or the evaluation set. The observed gain may therefore be the value of optimizing on the evaluation set rather than an intrinsic advantage of component selection over projection. The authors should either give the baselines the same type of label-informed selection (e.g., select projection dimensions by accuracy on a training split) or, more simply, report the selected subset's accuracy on a split not used during greedy selection. Without this, the central claim in the Abstract and Conclusion is unsupported.
- [§3.2 (retrieval task definition)] The benchmark's validity depends on the assumption in Section 3.2 that cosine similarity between the gradient of a paraphrased sample and its original is higher than to other training samples. The paper does not independently validate this assumption; it merely reports retrieval accuracy under the candidate set construction that always inserts the original sample (Appendix B.1, Algorithm 1). If the assumption fails, the retrieval task may be measuring arbitrary gradient similarity rather than training data influence, and the comparison would say little about explanations. A validation using a known influence signal (e.g., fine-tuning on inserted facts, or agreement with an established influence method) would strengthen the claim that the benchmark measures what the paper says it measures.
minor comments (5)
- [§4.1] Typo: 'We provides 0 as an example below' should be 'We provide s0 as an example below.'
- [§2, Related Work] 'proximal Bergmann response function' appears to be a typo for 'proximal Bregman response function.'
- [§5.3 and Figures 4–5] The accuracy curves are shown without error bars or repeated runs. Since the greedy selection is deterministic but the random projection may introduce variance, reporting standard errors over multiple projection seeds would clarify the comparison.
- [Table 2] The computational cost comparison is reported for the paraphrased setting only. It would be helpful to state explicitly whether the model-generated setting has the same profile, and to clarify the 'with caching' scenario's assumptions about memory and I/O.
- [Algorithm 2] The epsilon stability constant is added only to the denominator in the reconstructed similarity. Its effect on selected subsets and accuracy is not discussed; a small sensitivity analysis would be useful.
Circularity Check
Greedy selection is optimized on the exact evaluation set, making the headline retrieval gain a fitted objective rather than an out-of-sample result.
specific steps
-
fitted input called prediction
[Section 3.2 (retrieval metric), Section 3.3 / Algorithm 2 (selection objective), Section 5.3 (reported result)]
"At each step, we choose the next component index(l ∗, k∗)to add: (l∗, k∗) = arg max (l,k)∈W\S acc(b) S∪{(l,k)} (Dp, D) ... a← 1 N PN i=1 I[γ̂ S′ i,i > maxj∈Ci(b)\{i} γ̂ S′ i,j] ... Figure 4 shows that greedily selecting components based on retrieval accuracy identifies a small subset that significantly outperforms both random projection and the full gradient."
The component subset S is selected by Algorithm 2 to maximize acc(b) on the exact query set Dp (or Dm) and the exact candidate sets Ci(b) used for the results in Section 5. The reported accuracies are therefore the value of the selection objective, not held-out predictions. No train/validation split is described in Section 4 or 5; all 988 queries and their candidates are used both to choose components and to score them. The gain of 'Select' over 'Project' is the output of a search over 113 components on the evaluation data, so the comparison is between an optimized selector and a non-optimized baseline.
full rationale
The paper's central empirical claim—that greedily selected components capture training-data-influence information more effectively than the full gradient or random projection—rests on an in-sample optimization. Section 3.2 defines the retrieval accuracy acc(b)_θ(Dp,D) over query set Dp and BM25 candidate sets Ci(b). Section 3.3 and Algorithm 2 then choose components by maximizing exactly this acc(b) on the same Dp and Ci(b), using precomputed dot products. Section 5.3 reports those same accuracy curves as evidence of superiority. Because Algorithm 2 optimizes the evaluation metric itself and no held-out split is described, the reported 'prediction' that selection outperforms projection is the fitted objective value. This is a clear instance of fitted-input-called-prediction: the selected subset is a parameter fit to the evaluation data. The non-circular contributions—full-gradient behavior, single-component analyses, component-type/depth patterns, and the computational-cost comparison—may still stand, and the benchmark is a reasonable proposal, but the headline superiority claim requires held-out queries/candidates before it can support generalization. The Limitations section also concedes that generalization across architectures, scales, and domains was not explored. There is no load-bearing self-citation or definitional equivalence beyond this in-sample selection, so the score is 7 rather than higher.
Axiom & Free-Parameter Ledger
free parameters (4)
- candidate set size b =
5
- random projection dimension d =
1% and 5% of total parameters (not tuned)
- epsilon stability constant =
unspecified small positive
- selected component subset S =
e.g., <5% of parameters in paraphrased setting; achieving 0.998 accuracy in paraphrased and ~0.36 in model-generated
axioms (4)
- domain assumption Cosine similarity between gradients of a paraphrase and its original training sample is higher than to unrelated samples
- domain assumption Retrieval accuracy on paraphrased/model-generated queries is a valid proxy for instance-based explanation quality
- standard math Component-wise dot products sum to reconstruct cosine similarity for any subset
- domain assumption Results on a single 1.2B model and a 988-sample LIMA subset generalize
read the original abstract
Gradient-based methods for instance-based explanation for large language models (LLMs) are hindered by the immense dimensionality of model gradients. In practice, influence estimation is restricted to a subset of model parameters to make computation tractable, but this subset is often chosen ad hoc and rarely justified by systematic evaluation. This paper investigates if it is better to create low-dimensional representations by selecting a small, architecturally informed subset of model components or by projecting the full gradients into a lower-dimensional space. Using a novel benchmark, we show that a greedily selected subset of components captures the information about training data influence needed for a retrieval task more effectively than either the full gradient or random projection. We further find that this approach is more computationally efficient than random projection, demonstrating that targeted component selection is a practical strategy for making instance-based explanations of large models more computationally feasible.
Figures
Reference graph
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